HESSEMAT: Difference between revisions
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{{FILE|HESSEMAT}} defines the Hesse matrix in Cartesian coordinates (<math>\underline{\mathbf{H}}^\mathbf{x}</math> ) for the use in [[ | {{FILE|HESSEMAT}} defines the Hesse matrix in Cartesian coordinates (<math>\underline{\mathbf{H}}^\mathbf{x}</math> ) for the use in [[Thermodynamic integration#Thermodynamic integration with harmonic reference|Thermodynamic integration with harmonic reference]]. | ||
For a system containing <math> N</math> atoms, {{FILE|HESSEMAT}} has <math>(3N+1)(N+1)</math> lines. | For a system containing <math> N</math> atoms, {{FILE|HESSEMAT}} has <math>(3N+1)(N+1)</math> lines. | ||
The first line specifies potential energy <math>V_{0,\mathbf{x}}(\mathbf{x}_0)</math> (in eV) of the relaxed system for which <math>\underline{\mathbf{H}}^\mathbf{x}</math> is computed. | The first line specifies potential energy <math>V_{0,\mathbf{x}}(\mathbf{x}_0)</math> (in eV) of the relaxed system for which <math>\underline{\mathbf{H}}^\mathbf{x}</math> is computed. | ||
Revision as of 14:03, 17 October 2024
HESSEMAT defines the Hesse matrix in Cartesian coordinates ([math]\displaystyle{ \underline{\mathbf{H}}^\mathbf{x} }[/math] ) for the use in Thermodynamic integration with harmonic reference. For a system containing [math]\displaystyle{ N }[/math] atoms, HESSEMAT has [math]\displaystyle{ (3N+1)(N+1) }[/math] lines. The first line specifies potential energy [math]\displaystyle{ V_{0,\mathbf{x}}(\mathbf{x}_0) }[/math] (in eV) of the relaxed system for which [math]\displaystyle{ \underline{\mathbf{H}}^\mathbf{x} }[/math] is computed. The following [math]\displaystyle{ 3N }[/math] lines are reserved for positions in fractional coordinates of all atoms constituting the system, whereby each line should contain three components of position vector of a single atom. The remaining part of HESSEMAT consist of [math]\displaystyle{ 3N }[/math] block of [math]\displaystyle{ N+1 }[/math] lines each. Each block contains information related to a single eigenmode of [math]\displaystyle{ \underline{\mathbf{H}}^\mathbf{x} }[/math]: the first line specified the eigenvalue (in eV/[math]\displaystyle{ {\AA}^2 }[/math]) and remaining and [math]\displaystyle{ N }[/math] lines the corresponding eigenvector (in Cartesian coordinates) in a 3-column format.